ChapterZero

Today we started the second part of the applied functional analysis class: real analysis in . We jumped right in at Lebesgue outer measure, but considering that it’s on the syllabus, hopefully we’ll come back later after we develop Lebesgue theory to develop a more general theory of measure and integration. I like this approach: start with Lebesgue integration in , then do the abstract stuff. This is more effective than say Foland’s approach: do abstract integration, use it to establish Lebesgue integration in , and have an optional section on the theory in .

Now the notes from both parts of the course (1: functional analysis, 2: real analysis) are available– cf. the Lecture Notes section. They are comprehensive enough that I didn’t refer to the book at all for the first part, but I actually like the book for this part (Wheeden and Zygmund), so I’ll probably read along.